Simulating stress intensity factors for anisotropic materials by the least-squares method

Abstract

The main purpose of this paper is to investigate the accuracy of the least-squares method incorporating the finite element method for finding the stress intensity factors of composite materials. Numerical simulations in this paper indicate that the least-squares method can be used to calculate stress intensity factors accurately, if seven or eight displacements terms are included. The calculated stress intensity factors by using the least-squares method can be as accurate as the calculated J-integrals by using the J-integral formulation. If seven or eight displacement terms are included, the calculated stress intensity factors of this method are independent of the maximum radius of the area from which data is included; furthermore, a very fine mesh is also not necessary.

Accuracy and limit of a least-squares method to calculate 3D notch SIFs

“…The least-squares method has been applied to experimental and finite element methods for calculation of the SIFs of cracked bodies (Hyde and Warrior 1990; Ju 1996Ju , 1998Ju et al 2006). In this study, the leastsquares method incorporating the finite element analysis was employed to find the mixed-mode SIFs of a sharp V-notch.…”

Thermoelastic determination of crack-tip coordinates in composites

“…The stress and displacement fields around the crack-tip can be composed by these parameters. This method was first used to develop a singular element for cracked composite problems (Khalil et al, 1986), its reliability has been substantiated by comparing against results from the J-integral approach (Ju, 1996), and subsequently applied to determine stress intensity factors in orthotropic composites (Ju, 1996;Ju and Rowlands, 2003a,b).…”

“…Approximately 500-3000 simulated thermoelastic data points occur within the various data-acquisition areas (R max = 5-10 mm) employed, corresponding to a resolution in the region of interest of 0.1-0.3 mm between data points. The stress intensity factors (K I and K II ) for each of the three examples of cracked, orthotropic tensile-loaded plates were calculated using the method of the paper (Ju, 1996) for n = 8, Table 2. Unless stated otherwise, R max = a (2a = total crack length of a central crack, a = crack length) and R min = 0.2 mm.…”

Simulating three-dimensional stress intensity factors by the least-squares method

“…z "re F"r (cos #i sin ) (6) Along the crack surface, "$ , WX "0, and assume a H "b H #ib H>L , so (2c) changes to…”